• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Steel and Composite Structures
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• v.23 no.3
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• pp.251-261
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• 2017

In this paper, thermal effect on the vibration and stability of initially stressed sandwich plates with functionally graded material (FGM) face sheets is analyzed. Material properties of FGM face sheet are graded continuously in the thickness direction. The variation of FGM properties assumes a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of arbitrarily initially-stressed sandwich plates including the effects of transverse shear deformation and rotary inertia are derived. The initial stress is taken to be a combination of a uniaxial extensional stress and a pure bending stress in the examples. The eigenvalue problems are formed to study the vibration and buckling characteristics of simple supported initially stressed FGM/metal/FGM plates. The effects of volume fraction index, temperature rise, initial stress and layer thickness of metal on the natural frequencies and buckling loads are investigated. The results reveal that the volume fraction index, initial stresses and layer thickness of metal have significant influence on the vibration and stability of sandwich plates with FGM face sheets.

• The KSFM Journal of Fluid Machinery
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• v.19 no.5
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• pp.12-19
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• 2016

In present study, a parametric study of a centrifugal compressor with inlet treatment has been performed numerically using three-dimensional Reynolds-averaged Navier-Stokes equations. The shear stress transport turbulence model was used for analysis of turbulence. The finite volume method and unstructured grid system were used for the numerical solution. Tested parameters were related to the geometry of the inlet duct. It was found that the application of circumferentially distributed holes in the inlet duct improves operational stability of the compressor compared to that with conventional inlet duct.

• Steel and Composite Structures
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• v.18 no.6
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• pp.1541-1555
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• 2015

In this paper mechanical behavior of the functional gradient materials (FGM) micro-gripper under thermal load and DC voltage is numerically investigated taking into account the effect of intermolecular forces. In contrary to the similar previous works, which have been conducted for homogenous material, here, the FGM material has been implemented. It is assumed that the FGM micro-gripper is made of metal and ceramic and that material properties are changed continuously along the beam thickness according to a given function. The nonlinear governing equations of the static and dynamic deflection of microbeams have been derived using the coupled stress theory. The equations have been solved using the Galerkin based step-by-step linearization method (SSLM). The solution procedure has been evaluated against available data of literature showing good agreement. A parametric study has been conducted, focusing on the combined effects of important parameters included DC voltage, temperature variation, geometrical dimensions and ceramic volume concentration on the dynamic response and stability of the FGM micro-gripper.

• Geomechanics and Engineering
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• v.13 no.2
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• pp.353-370
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• 2017

This paper presents a case study and numerical investigation to study the hydro-mechanical response of a shallow landslide in unsaturated slopes subjected to rainfall infiltration using a coupled model. The coupled model was interpreted in details by expressing the balance equations for soil mixture and the coupled constitutive equations. The coupled model was verified against experimental data from the shearing-infiltration triaxial tests. A real case of shallow landslide occurred on Mt. Umyeonsan, Seoul, Korea was employed to explore the influence of rainfall infiltration on the slope stability during heavy rainfall. Numerical results showed that the coupled model accurately predicted the poromechanical behavior of a rainfall-induced landslide by simultaneously linking seepage and stress-strain problems. It was also found that the coupled model properly described progress failure of a slope in a highly transient condition. Through the comparisons between the coupled and uncoupled models, the coupled model provided more realistic analysis results under rainfall. Consequently, the coupled model was found to be feasible for the stability and seepage analysis of practical engineering problems.

• Ecology and Resilient Infrastructure
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• v.1 no.1
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• pp.29-38
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• 2014

This study analyzed shear stress and erosion characteristic of a vegetated levee embankment with root fiber quantity, which is an important factor for evaluating the stability of it. The averaged root fiber quantity in a vegetated levee revetment was measured by the sampler manufactured by this research. The Phragmites Japonica Steud which is somewhat dominant species in a vegetated levee embankment was selected as an experimental vegetation. As a result of experiment of each flow regime, the shear stress was increased while root fiber quantity was increased and the erosion rate was exponentially decreased as the root fiber quantity was increased. The erosion rate was exponentially decreased as the shear stress was increased which is shown that the increase of shear stress by root fiber quantity results in the increase of erosion resistance in a vegetated soil. The relationship between shear stress and erosion rate with root fiber quantity were analyzed and their regression equations were suggested with high determination coefficients. The hydraulic stability is governed by the increase of shear stress by root fiber quantity and the Froude number of flow characteristic in a vegetated levee revetment.

• Macromolecular Research
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• v.9 no.3
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• pp.164-170
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• 2001

Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.465-476
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• 2018

This article investigates buckling behavior of a multi-phase nanocrystalline nanobeam resting on Winkler-Pasternak foundation in the framework of nonlocal couple stress elasticity and a higher order refined beam model. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, and couple stress effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical approach. The buckling loads are compared with those of nonlocal couple stress-based beams. It is showed that buckling loads of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, shear deformation, surface effect, nonlocality and boundary conditions.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.423-434
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• 2018

In present work, both the hyperbolic shear deformation theory and stress function concept are used to study the mechanical and thermal stability responses of functionally graded (FG) plates resting on elastic foundation. The accuracy of the proposed formulation is checked by comparing the computed results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed formulation can achieve the same accuracy of the existing HSDTs which have more number of governing equations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1001-1008
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• 2006

The main objective of this paper is to compare economical effectiveness of typical methods for checking stability in principal components of steel cable-stayed bridges. Elastic and inelastic buckling analyses are carried out for frame-like numerical models of cable-stayed bridges. The axial-flexural interaction equations prescribed in AASHTO Allowable Stress Design (ASD) and AASHTO Load and Resistance Factor Design (LRFD) are used in order to check the stability of principal components. Parametric studies are performed for numerical models which have the center span length of 300m, 600m, 900m and l200m with different girder depths. Peak values of the interaction equations are calculated at the intersection point between girders and towers. These peak values are considered as a major factor to design of principal components of cable-stayed bridges. As a result, more economical design for girders and towers can be feasible using the inelastic buckling analysis. In addition, LRFD codes are more economical about 20% on the average than ASD codes for all numerical models of cable-stayed bridges.